Infinite Spring-Mass Chain Model Using Fibonacci Wave Functions

This paper presents new general model for spring-mass chain using Fibonacci wave functions. This general model will be derived from a simple first order mechanical mass-viscous damper. The Fibonacci wave function of the nth order spring-mass chain will be easily determined from Pascal's triangle new general form for its numerator and denominator. This model can be generated to an infinite order; each section in the chain is precisely defined by its Fibonacci wave function order with speed-force or momentum-position variables. The spring mass chain model can also be expressed in the form of energy transfer between each section. Applications like particle interaction in quantum mechanics or in fluid mechanics can be analyzed using this new proposed model. Spring-mass chain with no damping resistance or with infinite damping resistance is also derived easily from Pascal's triangle general form.